By surface analysis, ръмя́ (rǎmjá, “to mizzle”) + -еж (-ež).
ръме́ж • (rǎméž) m
- drizzle, mizzle (misty rain)
- “ръмеж”, in Речник на българския език [Dictionary of the Bulgarian Language] (in Bulgarian), Sofia: Bulgarian Academy of Sciences, 2014
- “ръмеж”, in Речник на българския език [Dictionary of the Bulgarian Language] (in Bulgarian), Chitanka, 2010